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In the recent years, the thermal Hall transport has risen as an important diagnosis of the physical properties of the elementary excitations in various quantum materials, especially among the Mott insulating systems where the electronic transports are often featureless. Here we review the recent development of thermal Hall effects in quantum magnets where all the relevant excitations are charge-neutral. In addition to summarizing the existing experiments, we pay a special attention to the underlying mechanisms of the thermal Hall effects in various magnetic systems, and clarify the connection between the microscopic physical variables and the emergent degrees of freedom in different quantum phases. The external magnetic field is shown to modify the intrinsic Berry curvature properties of various emergent and/or exotic quasiparticle excitations in distinct fashions for different quantum systems and quantum phases, contributing to the thermal Hall transports. These include, for example, the conventional ones like the magnons in ordered magnets, the triplons in dimerized magnets, the exotic and fractionalized quasiparticles such as the spinons and the magnetic monopoles in quantum spin liquids. We review their contribution and discuss their presence in the thermal Hall conductivity in different physical contexts. We expect this review to provide a useful guidance for the physical mechanism of the thermal Hall transports in quantum magnets. [ABSTRACT FROM AUTHOR]

Computational modules were developed to numerically determine electronic band structures, berry curvatures, Chern numbers, localization lengths, and critical exponents for tight- binding and related models. These modules were applied to a variety tight-binding and related models including the Hofstadter Model, Anderson Model, and the Chalker- Coddington model. When analytic solutions were available, numeric energy bands agreed with analytic solutions to within machine precision. In addition Chern numbers for well known models were reproduced, and localization lengths and critical exponents agreed with values in the literature.

We propose a method for broadband long-wavelength photodetection using the nonlinear Hall effect in noncentrosymmetric quantum materials. The inherently quadratic relation between transverse current and input voltage at zero magnetic field is used to rectify the incident terahertz or infrared electric field into a direct current, without invoking any diode. Our photodetector operates at zero external bias with fast response speed and has zero threshold voltage. Remarkably, the intrinsic current responsivity due to the Berry curvature mechanism is a material property independent of the incident frequency or the scattering rate, which can be evaluated from first-principles electronic structure calculations. We identify the Weyl semimetal NbP and ferroelectric semiconductor GeTe for terahertz/infrared photodetection with large current responsivity without external bias. [ABSTRACT FROM AUTHOR]

Geometrical phases, such as the Berry phase, have proven to be powerful concepts to understand numerous physical phenomena, from the precession of the Foucault pendulum to the quantum Hall effect and the existence of topological insulators. The Berry phase is generated by a quantity named the Berry curvature, which describes the local geometry of wave polarization relations and is known to appear in the equations of motion of multi-component wave packets. Such a geometrical contribution in ray propagation of vectorial fields has been observed in condensed matter, optics and cold atom physics. Here, we use a variational method with a vectorial Wentzel–Kramers–Brillouin ansatz to derive ray- tracing equations for geophysical waves and to reveal the contribution of the Berry curvature. We detail the case of shallow-water wave packets and propose a new interpretation of their oscillating motion around the equator. Our result shows a mismatch with the textbook scalar approach for ray tracing, by predicting a larger eastward velocity for Poincaré wave packets. This work enlightens the role of the geometry of wave polarization in various geophysical and astrophysical fluid waves, beyond the shallow-water model. [ABSTRACT FROM AUTHOR]

We consider a film of a topological insulator (TI) sandwiched between two ferromagnetic (FM) layers. The system is additionally under an external gate voltage. The surface electron states of TI are magnetized due to the magnetic proximity effect to the ferromagnetic layers. The magnetization of ferromagnetic layers can be changed by applying an external magnetic field or by varying thickness of the topological insulator (owing to the interlayer exchange coupling). The change in the magnetic configuration of the system affects the transport properties of the surface electronic states. Using the Green function formalism, we calculate spin polarization, anomalous Hall effect, and magnetoresistance of the system. We show, among others, that by tuning the gate voltage and magnetizations of the top and bottom FM layers, one can observe the topological transition to the quantum anomalous Hall state. • A topological insulator sandwiched between ferromagnetic layers is considered. • Two magnetization configurations of layers (parallel and antiparallel) are studied. • Switching between trivial and topological insulator state under gate voltage is discussed. [ABSTRACT FROM AUTHOR]

We propose an experimental scheme to simulate the many-body dynamical quantum Hall effect with ultra-cold bosonic atoms in a one-dimensional optical lattice. We first show that the required model Hamiltonian of a spin-1/2 Heisenberg chain with an effective magnetic field and tunable parameters can be realized in this system. For dynamical response to ramping the external fields, the quantized plateaus emerge in the Berry curvature of the interacting atomic spin chain as a function of the effective spin-exchange interaction. The quantization of this response in the parameter space with the interaction-induced topological transition characterizes the many-body dynamical quantum Hall effect. Furthermore, we demonstrate that this phenomenon can be observed in practical cold atom experiments with numerical simulations. [ABSTRACT FROM AUTHOR]

Geometric phases in quantum mechanics play an extraordinary role in broadening our understanding of fundamental significance of geometry in nature. One of the best known examples is the Berry phase [M.V. Berry (1984), Proc. Royal. Soc. London A, 392:45], which naturally emerges in quantum adiabatic evolution. So far the applicability and measurements of the Berry phase were mostly limited to systems of weakly interacting quasi-particles, where interference experiments are feasible. Here we show how one can go beyond this limitation and observe the Berry curvature, and hence the Berry phase, in generic systems as a nonadiabatic response of physical observables to the rate of change of an external parameter. These results can be interpreted as a dynamical quantum Hall effect in a parameter space. The conventional quantum Hall effect is a particular example of the general relation if one views the electric field as a rate of change of the vector potential. We illustrate our findings by analyzing the response of interacting spin chains to a rotating magnetic field. We observe the quantization of this response, which we term the rotational quantum Hall effect. [ABSTRACT FROM AUTHOR]

Abstract: We describe an intrinsic spin-Hall effect (SHE) in n-type bulk zinc-blende semiconductors with a topological origin. When a collimated flux of electrons is injected into a zinc-blende semiconductor with Dresselhaus spin–orbit interaction, a nontrivial gauge structure appears in the momentum space of the electrons. The Berry curvature of this gauge field and the corresponding Lorentz force in -space results in a finite SHE. The value of the spin-Hall current is found to be highly dependent on the degree of electron collimation, which may be varied by means of gate electrodes. Therefore, the system may potentially be useful as an electronically controllable source of pure spin-current for spintronic applications. [Copyright &y& Elsevier]

• WSe 2 monolayer: a Dirac half-metal without SOC and a Chern insulator with SOC. • WSe 2 monolayer shows nonzero Chern number, QAHC, and gapless chiral edge states. • WSe 2 monolayer is an excellent 2D candidate for QAHE under high temperature. Quantum anomalous Hall (QAH) effect presents a promising platform for next generation nano-electronics due to its dissipationless edge states. Unfortunately, until now, QAH materials suitable for practical applications are rare. Based on the first-principles calculations, we found a novel two-dimensional (2D) QAH insulator: WSe 2 monolayer. Both the spin-polarized electronic structure and spin-orbit coupling (SOC) of WSe 2 contribute to the QAH effect. When SOC is ignored, the WSe 2 monolayer is a spin-polarized Dirac half-metal (DHM). Taking SOC into account, a global band gap about 30 meV is opened and the system behaves as an intrinsic Chern insulator with a Curie temperature of 160 K. The non-trivial properties are proved by the nonzero Chern number, quantized anomalous Hall conductivity, and gapless chiral edge states. We expect the material will become a promising candidate for realizing the QAH effect with higher experimental temperature. [ABSTRACT FROM AUTHOR]